On entropies of block-gluing subshifts

12/17/2020

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by   Svetlana Puzynina, et al.

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A subshift X is called c-block gluing if for any integer n≥ c and any two blocks u and v from the language of X there exists an element of X which has occurrences of u and v at distance n. In this note we study the topological entropies of c-block gluing binary one-dimensional subshifts. We define the set R_c to be the set of entropies of all c-block-gluing subshifts, and R=∪_c∈ℕ R_c. We show that the set R is dense, while R_1 and R_2 are not; in particular, they have isolated points. We conjecture that the same holds for any c.